Don't know much about Pol Sci or Sociology, but for economics, PhD coursework requires high level mathematics abilities such as calculus, linear algebra, trigonometry, econometrics, statistics, real analysis etc, which I presume you don't possess given that you have done atleast 6 years of legal education. So I think you should think about Econ PhD atleast.
If I have a LLM degree, can I pursue a PhD in another field ? Example Pol Sci, Economics, Sociology ? Do I have to only pursue PhD in law to avail JRF Law ?
Many times, not even in law.
Pol Sci would be a good match with law.